CAT QA Preparation of Binomial Theorem: Check Important Formulas, and Solved Sample Questions

CAT Binomial Theorem is a part of the Quantitative Aptitude section. In CAT Question Paper, questions will not be directly asked from Binomial Theorem but will be based on the concepts of the topic. Candidates can easily solve such questions if they have gone through the basic concepts once. From CAT Quantitative Aptitude Syllabus a total of 34 questions will be asked and around 8-7 questions will be TITA type. With a proper CAT Preparation plan candidates can easily cover all the topics along with the practice of MCQ and TITA questions. 

Binomial expansion is used for two variables and if the number of variables to be expanded is more than two, then it is called multinomial expansion. The aim of both the formulas is to simplify the solution that would otherwise be complicated. Read the article to know more about the concept, formulas and solved questions to prepare for CAT. 

CAT Preparation: Learning Binomial Theorem Formulas

The formula for Binomial Theorem is:

(x + y)n = nΣr=0 nCr xn – r · yr

In the formula mentioned above, note that:

Here are a few points to remember:

1. nC0, nC1,..., nCn are known as binomial coefficients. The other way to represent them is C0, C1,..., Cn
2. (n+1) is always the total number of terms in (x+y)n
3. N is always the sum of x and y.
4. In case “n” is an odd figure, (x + b)n + (x - b)n and (x + b)n - (x - b)n will have the number of terms as equal to (n + 1)/2
5. In case “n” is an even figure, (x + b)n + (x - b)n would have (n + 1)/2 as the number of terms and (x + b)n - (x - b)n will have n/2 as the number of terms.

Download CAT Sample Papers:

• CAT Previous Year Question Papers of Quant
• CAT Previous Year Question Papers of DILR
• CAT Previous Year Question Papers of VARC

CAT Previous Years Solved Sample Questions on Binomial Theorems

Question 1: By using the Binomial Theorem, expand (2x-3)^6.

Answer 1:

Question 2: What is the coefficient of x^5 in the expansion of (1 + x^2)^5 (1 + x)^4?

1. 40
2. 50
3. -50
4. 60

Answer 2:

Question 3: Which is the last digit of (32)^32?

1. 4
2. 6
3. 8
4. None of the above

Answer 3:

Question 4: What is (√3 + 1)2n – (√3 – 1)2n if n is a positive integer?

1. An irrational number
2. An odd positive number
3. An even positive number
4. A rational number other than positive integers.

Answer 4:

Quick Links:

• Check CAT Exam Pattern
• Best Books for CAT Preparation

Question 5: Which is the greatest numerical term in the expansion of (2 + 3x)^9 if the value of x is 3/2?

1. (5 x 3^11)/2
2. (5 x 3^13)/2
3. (7 x 3^13)/2
4. None of the above

Answer:

Question 6: Which is the largest: 99^50 + 100^50 or 101^50?

1. 101^50
2. 99^50 + 100^50
3. Both have equal value
4. None of the above

Answer 6:

Question 7: What would be the remainder if 7^103 is divided by 25?

1. 20
2. 16
3. 18
4. 15

Answer 7:

Question 8: The middle term of (4 + 2x)^6 is:

1. 11240 x^2
2. 10240 x^3
3. 12240 x^4
4. 10340 x^4

Answer 8:

Question 9: Assuming that the general term is ^91C2 x^89, what would be the expansion?

1. x^91
2. (x - 2)^90
3. (x - 1)^91
4. (x + 1)^90

Answer 9:

Question 10: What will be the middle term of (xyz - x)^2n?

1. (n + 1)th term
2. (n + 2)th term
3. nth term
4. (n - 1)th term

Answer 10:

Question 11: The fourth term of (x - 5y)^96 is:

1. 125 ^96C3 x^93 y^3
2. 625 ^96C3 x^93 y^4
3. 625 ^96C4 x^93 y^4
4. 125 ^96C4 x^93 y^4

Answer 11:

CAT Study Material Quick Links: